TSTP Solution File: SEU166+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:07:30 EDT 2022
% Result : Theorem 0.57s 0.98s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 285 ( 123 unt; 18 typ; 0 def)
% Number of atoms : 2153 ( 844 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 5927 (1021 ~; 792 |; 38 &;4060 @)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 955 ( 0 ^ 947 !; 8 ?; 955 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartesian_product2,type,
cartesian_product2: $i > $i > $i ).
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_sK10_SY30,type,
sK10_SY30: $i > $i > $i > $i ).
thf(tp_sK11_SY32,type,
sK11_SY32: $i > $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY24,type,
sK2_SY24: $i ).
thf(tp_sK3_SY26,type,
sK3_SY26: $i ).
thf(tp_sK4_A,type,
sK4_A: $i ).
thf(tp_sK5_A,type,
sK5_A: $i ).
thf(tp_sK6_C,type,
sK6_C: $i > $i > $i ).
thf(tp_sK7_E,type,
sK7_E: $i > $i > $i > $i > $i ).
thf(tp_sK8_SY27,type,
sK8_SY27: $i > $i > $i > $i > $i ).
thf(tp_sK9_D,type,
sK9_D: $i > $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(2,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(3,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(10,conjecture,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
thf(11,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ C ) )
& ( subset @ ( cartesian_product2 @ C @ A ) @ ( cartesian_product2 @ C @ B ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[11]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( cartesian_product2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i,F: $i] :
( ( in @ E @ A )
& ( in @ F @ B )
& ( D
= ( ordered_pair @ E @ F ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [SY24: $i,SY25: $i] :
( ( subset @ sK1_A @ SY24 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ SY25 ) @ ( cartesian_product2 @ SY24 @ SY25 ) )
& ( subset @ ( cartesian_product2 @ SY25 @ sK1_A ) @ ( cartesian_product2 @ SY25 @ SY24 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).
thf(23,plain,
( ( ! [SY26: $i] :
( ( subset @ sK1_A @ sK2_SY24 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ SY26 ) )
& ( subset @ ( cartesian_product2 @ SY26 @ sK1_A ) @ ( cartesian_product2 @ SY26 @ sK2_SY24 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[22]) ).
thf(24,plain,
( ( ( subset @ sK1_A @ sK2_SY24 )
=> ( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) )
& ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[23]) ).
thf(25,plain,
( ( subset @ sK1_A @ sK2_SY24 )
= $true ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(26,plain,
( ( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) )
& ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[24]) ).
thf(27,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[26]) ).
thf(28,plain,
( ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[26]) ).
thf(29,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(31,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(32,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(33,plain,
( ( empty @ sK5_A )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK6_C @ B @ A ) @ A )
& ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(35,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY28: $i,SY29: $i] :
( ~ ( in @ SY28 @ A )
| ~ ( in @ SY29 @ B )
| ( ( sK9_D @ C @ B @ A )
!= ( ordered_pair @ SY28 @ SY29 ) ) )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK10_SY30 @ C @ B @ A ) @ A )
& ( in @ ( sK11_SY32 @ C @ B @ A ) @ B )
& ( ( sK9_D @ C @ B @ A )
= ( ordered_pair @ ( sK10_SY30 @ C @ B @ A ) @ ( sK11_SY32 @ C @ B @ A ) ) ) )
| ( in @ ( sK9_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK7_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK8_SY27 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK7_E @ D @ C @ B @ A ) @ ( sK8_SY27 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY28: $i,SY29: $i] :
( ~ ( in @ SY28 @ A )
| ~ ( in @ SY29 @ B )
| ( ( sK9_D @ C @ B @ A )
!= ( ordered_pair @ SY28 @ SY29 ) ) )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK10_SY30 @ C @ B @ A ) @ A )
& ( in @ ( sK11_SY32 @ C @ B @ A ) @ B )
& ( ( sK9_D @ C @ B @ A )
= ( ordered_pair @ ( sK10_SY30 @ C @ B @ A ) @ ( sK11_SY32 @ C @ B @ A ) ) ) )
| ( in @ ( sK9_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK7_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK8_SY27 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK7_E @ D @ C @ B @ A ) @ ( sK8_SY27 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(40,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK6_C @ B @ A ) @ A )
& ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(43,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(44,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(45,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(46,plain,
( ( subset @ sK1_A @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(47,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK9_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK11_SY32 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK9_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK10_SY30 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY32 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_SY27 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK7_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY27 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(49,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY33: $i] :
( ~ ( in @ SV1 @ SY33 )
| ~ ( in @ SY33 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY34: $i] :
( ( unordered_pair @ SV2 @ SY34 )
= ( unordered_pair @ SY34 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY35: $i] :
( ( ordered_pair @ SV3 @ SY35 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SY35 ) @ ( singleton @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(53,plain,
! [SV4: $i] :
( ( ! [SY36: $i] :
~ ( empty @ ( ordered_pair @ SV4 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(54,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(55,plain,
! [SV5: $i] :
( ( subset @ SV5 @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(56,plain,
( ( subset @ ( cartesian_product2 @ sK1_A @ sK3_SY26 ) @ ( cartesian_product2 @ sK2_SY24 @ sK3_SY26 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(57,plain,
! [SV6: $i] :
( ( ~ ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ( ! [SY39: $i,SY40: $i] :
( ~ ( in @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SY37 )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ~ ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) @ SY37 ) )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) ) )
| ( SY38
= ( cartesian_product2 @ SV6 @ SY37 ) ) )
| ~ ! [SY41: $i,SY42: $i] :
( ( SY42
!= ( cartesian_product2 @ SV6 @ SY41 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i,SY45: $i] :
( ~ ( in @ SY44 @ SV6 )
| ~ ( in @ SY45 @ SY41 )
| ( SY43
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY43 @ SY42 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY42 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) @ SY41 ) )
| ( SY46
!= ( ordered_pair @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(58,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(59,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( in @ SV1 @ SV7 )
| ~ ( in @ SV7 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(60,plain,
! [SV8: $i,SV2: $i] :
( ( ( unordered_pair @ SV2 @ SV8 )
= ( unordered_pair @ SV8 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(61,plain,
! [SV9: $i,SV3: $i] :
( ( ( ordered_pair @ SV3 @ SV9 )
= ( unordered_pair @ ( unordered_pair @ SV3 @ SV9 ) @ ( singleton @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(62,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV4 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(63,plain,
! [SV6: $i] :
( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ( ! [SY39: $i,SY40: $i] :
( ~ ( in @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SY37 )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ~ ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) @ SY37 ) )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) ) )
| ( SY38
= ( cartesian_product2 @ SV6 @ SY37 ) ) )
| ~ ! [SY41: $i,SY42: $i] :
( ( SY42
!= ( cartesian_product2 @ SV6 @ SY41 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i,SY45: $i] :
( ~ ( in @ SY44 @ SV6 )
| ~ ( in @ SY45 @ SY41 )
| ( SY43
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY43 @ SY42 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY42 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) @ SY41 ) )
| ( SY46
!= ( ordered_pair @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(64,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(65,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(66,plain,
! [SV7: $i,SV1: $i] :
( ( ( ~ ( in @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV10: $i,SV4: $i] :
( ( empty @ ( ordered_pair @ SV4 @ SV10 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV6: $i] :
( ( ~ ! [SY37: $i,SY38: $i] :
( ~ ( ~ ( ! [SY39: $i,SY40: $i] :
( ~ ( in @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SY37 )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ~ ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) @ SY37 ) )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) ) )
| ( SY38
= ( cartesian_product2 @ SV6 @ SY37 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV6: $i] :
( ( ~ ! [SY41: $i,SY42: $i] :
( ( SY42
!= ( cartesian_product2 @ SV6 @ SY41 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i,SY45: $i] :
( ~ ( in @ SY44 @ SV6 )
| ~ ( in @ SY45 @ SY41 )
| ( SY43
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY43 @ SY42 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY42 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) @ SY41 ) )
| ( SY46
!= ( ordered_pair @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(72,plain,
! [SV7: $i,SV1: $i] :
( ( ( in @ SV1 @ SV7 )
= $false )
| ( ( ~ ( in @ SV7 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ( ~ ( ! [SY39: $i,SY40: $i] :
( ~ ( in @ SY39 @ SV6 )
| ~ ( in @ SY40 @ SY37 )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ SY39 @ SY40 ) ) )
| ~ ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) @ SY37 ) )
| ( ( sK9_D @ SY38 @ SY37 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SY38 @ SY37 @ SV6 ) @ ( sK11_SY32 @ SY38 @ SY37 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SY38 @ SY37 @ SV6 ) @ SY38 ) ) )
| ( SY38
= ( cartesian_product2 @ SV6 @ SY37 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(74,plain,
! [SV6: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( SY42
!= ( cartesian_product2 @ SV6 @ SY41 ) )
| ~ ( ~ ! [SY43: $i] :
( ! [SY44: $i,SY45: $i] :
( ~ ( in @ SY44 @ SV6 )
| ~ ( in @ SY45 @ SY41 )
| ( SY43
!= ( ordered_pair @ SY44 @ SY45 ) ) )
| ( in @ SY43 @ SY42 ) )
| ~ ! [SY46: $i] :
( ~ ( in @ SY46 @ SY42 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) @ SY41 ) )
| ( SY46
!= ( ordered_pair @ ( sK7_E @ SY46 @ SY42 @ SY41 @ SV6 ) @ ( sK8_SY27 @ SY46 @ SY42 @ SY41 @ SV6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV11: $i] :
( ( ! [SY47: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SY47 @ SV11 ) @ SV11 )
| ~ ~ ( in @ ( sK6_C @ SY47 @ SV11 ) @ SY47 ) )
| ( subset @ SV11 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV12: $i] :
( ( ! [SY48: $i] :
( ~ ( subset @ SV12 @ SY48 )
| ! [SY49: $i] :
( ~ ( in @ SY49 @ SV12 )
| ( in @ SY49 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( in @ SV1 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV13: $i,SV6: $i] :
( ( ! [SY50: $i] :
( ~ ( ~ ( ! [SY51: $i,SY52: $i] :
( ~ ( in @ SY51 @ SV6 )
| ~ ( in @ SY52 @ SV13 )
| ( ( sK9_D @ SY50 @ SV13 @ SV6 )
!= ( ordered_pair @ SY51 @ SY52 ) ) )
| ~ ( in @ ( sK9_D @ SY50 @ SV13 @ SV6 ) @ SY50 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY50 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SY50 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SY50 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SY50 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SY50 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SY50 @ SV13 @ SV6 ) @ SY50 ) ) )
| ( SY50
= ( cartesian_product2 @ SV6 @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY53: $i] :
( ( SY53
!= ( cartesian_product2 @ SV6 @ SV14 ) )
| ~ ( ~ ! [SY54: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY54
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY54 @ SY53 ) )
| ~ ! [SY57: $i] :
( ~ ( in @ SY57 @ SY53 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY57 @ SY53 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY57 @ SY53 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY57
!= ( ordered_pair @ ( sK7_E @ SY57 @ SY53 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY57 @ SY53 @ SV14 @ SV6 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV11: $i,SV15: $i] :
( ( ~ ( ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV11 )
| ~ ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 ) )
| ( subset @ SV11 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ( subset @ SV12 @ SV16 )
| ! [SY58: $i] :
( ~ ( in @ SY58 @ SV12 )
| ( in @ SY58 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(82,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ~ ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) ) )
| ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV14: $i,SV6: $i,SV18: $i] :
( ( ( SV18
!= ( cartesian_product2 @ SV6 @ SV14 ) )
| ~ ( ~ ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV11 )
| ~ ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 ) ) )
= $true )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( subset @ SV12 @ SV16 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ SV12 )
| ( in @ SY58 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) ) ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV14: $i,SV6: $i,SV18: $i] :
( ( ( ( SV18
!= ( cartesian_product2 @ SV6 @ SV14 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV11 )
| ~ ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 ) )
= $false )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV16: $i,SV12: $i] :
( ( ( subset @ SV12 @ SV16 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ SV12 )
| ( in @ SY58 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(90,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV14: $i,SV6: $i,SV18: $i] :
( ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV11 ) )
= $false )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(93,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 ) )
= $false )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[88]) ).
thf(94,plain,
! [SV16: $i,SV12: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV12 )
| ( in @ SV19 @ SV16 ) )
= $true )
| ( ( subset @ SV12 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( ~ ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(96,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) ) )
= $false )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[90]) ).
thf(97,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) )
| ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(98,plain,
! [SV11: $i,SV15: $i] :
( ( ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV11 )
= $true )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
! [SV11: $i,SV15: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 ) )
= $true )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(100,plain,
! [SV16: $i,SV12: $i,SV19: $i] :
( ( ( ~ ( in @ SV19 @ SV12 ) )
= $true )
| ( ( in @ SV19 @ SV16 )
= $true )
| ( ( subset @ SV12 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) )
| ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(102,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
| ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(103,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ~ ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(104,plain,
! [SV6: $i,SV14: $i,SV18: $i] :
( ( ( ~ ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[97]) ).
thf(105,plain,
! [SV11: $i,SV15: $i] :
( ( ( in @ ( sK6_C @ SV15 @ SV11 ) @ SV15 )
= $false )
| ( ( subset @ SV11 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV16: $i,SV12: $i,SV19: $i] :
( ( ( in @ SV19 @ SV12 )
= $false )
| ( ( in @ SV19 @ SV16 )
= $true )
| ( ( subset @ SV12 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV17: $i,SV13: $i,SV6: $i] :
( ( ( ! [SY59: $i,SY60: $i] :
( ~ ( in @ SY59 @ SV6 )
| ~ ( in @ SY60 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SY59 @ SY60 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(108,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ! [SY61: $i] :
( ! [SY55: $i,SY56: $i] :
( ~ ( in @ SY55 @ SV6 )
| ~ ( in @ SY56 @ SV14 )
| ( SY61
!= ( ordered_pair @ SY55 @ SY56 ) ) )
| ( in @ SY61 @ SV18 ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV6: $i,SV14: $i,SV18: $i] :
( ( ( ! [SY64: $i] :
( ~ ( in @ SY64 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SY64
!= ( ordered_pair @ ( sK7_E @ SY64 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SY64 @ SV18 @ SV14 @ SV6 ) ) ) ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(111,plain,
! [SV17: $i,SV13: $i,SV6: $i,SV20: $i] :
( ( ( ! [SY65: $i] :
( ~ ( in @ SV20 @ SV6 )
| ~ ( in @ SY65 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SY65 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV6: $i] :
( ( ( ! [SY66: $i,SY67: $i] :
( ~ ( in @ SY66 @ SV6 )
| ~ ( in @ SY67 @ SV14 )
| ( SV21
!= ( ordered_pair @ SY66 @ SY67 ) ) )
| ( in @ SV21 @ SV18 ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV18 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SV22
!= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(115,plain,
! [SV17: $i,SV13: $i,SV23: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV6 )
| ~ ( in @ SV23 @ SV13 )
| ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(117,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[112]) ).
thf(118,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV6: $i] :
( ( ( ! [SY66: $i,SY67: $i] :
( ~ ( in @ SY66 @ SV6 )
| ~ ( in @ SY67 @ SV14 )
| ( SV21
!= ( ordered_pair @ SY66 @ SY67 ) ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(119,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ SV22 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SV22
!= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(120,plain,
! [SV17: $i,SV13: $i,SV23: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV6 )
| ~ ( in @ SV23 @ SV13 ) )
= $true )
| ( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(122,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
= ( ordered_pair @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV6: $i,SV24: $i] :
( ( ( ! [SY68: $i] :
( ~ ( in @ SV24 @ SV6 )
| ~ ( in @ SY68 @ SV14 )
| ( SV21
!= ( ordered_pair @ SV24 @ SY68 ) ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( in @ SV22 @ SV18 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SV22
!= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) ) ) )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV17: $i,SV13: $i,SV23: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( in @ SV20 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV23 @ SV13 ) )
= $true )
| ( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(126,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(127,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV25: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV6 )
| ~ ( in @ SV25 @ SV14 )
| ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
| ( SV22
!= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV17: $i,SV13: $i,SV23: $i,SV6: $i,SV20: $i] :
( ( ( in @ SV20 @ SV6 )
= $false )
| ( ( ~ ( in @ SV23 @ SV13 ) )
= $true )
| ( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(131,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( ~ ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 ) )
= $false )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[126]) ).
thf(132,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV25: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV6 )
| ~ ( in @ SV25 @ SV14 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(133,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(134,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ( SV22
!= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(135,plain,
! [SV17: $i,SV6: $i,SV20: $i,SV13: $i,SV23: $i] :
( ( ( in @ SV23 @ SV13 )
= $false )
| ( ( in @ SV20 @ SV6 )
= $false )
| ( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
!= ( ordered_pair @ SV20 @ SV23 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(136,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( in @ ( sK10_SY30 @ SV17 @ SV13 @ SV6 ) @ SV6 )
= $true )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(137,plain,
! [SV6: $i,SV13: $i,SV17: $i] :
( ( ( in @ ( sK11_SY32 @ SV17 @ SV13 @ SV6 ) @ SV13 )
= $true )
| ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(138,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV25: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( in @ SV24 @ SV6 ) )
= $true )
| ( ( ~ ( in @ SV25 @ SV14 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) ) )
= $true )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(140,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( SV22
= ( ordered_pair @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) ) )
= $true )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(141,plain,
! [SV23: $i,SV20: $i,SV6: $i,SV13: $i,SV17: $i] :
( ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
= ( ordered_pair @ SV20 @ SV23 ) )
= $false )
| ( ( in @ SV20 @ SV6 )
= $false )
| ( ( in @ SV23 @ SV13 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 ) )
= $true )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(142,plain,
! [SV18: $i,SV21: $i,SV14: $i,SV25: $i,SV6: $i,SV24: $i] :
( ( ( in @ SV24 @ SV6 )
= $false )
| ( ( ~ ( in @ SV25 @ SV14 ) )
= $true )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(143,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
| ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(144,plain,
! [SV20: $i,SV23: $i,SV6: $i,SV13: $i,SV17: $i] :
( ( ( in @ ( sK9_D @ SV17 @ SV13 @ SV6 ) @ SV17 )
= $false )
| ( ( in @ SV23 @ SV13 )
= $false )
| ( ( in @ SV20 @ SV6 )
= $false )
| ( ( ( sK9_D @ SV17 @ SV13 @ SV6 )
= ( ordered_pair @ SV20 @ SV23 ) )
= $false )
| ( ( SV17
= ( cartesian_product2 @ SV6 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV18: $i,SV21: $i,SV6: $i,SV24: $i,SV14: $i,SV25: $i] :
( ( ( in @ SV25 @ SV14 )
= $false )
| ( ( in @ SV24 @ SV6 )
= $false )
| ( ( ( SV21
!= ( ordered_pair @ SV24 @ SV25 ) ) )
= $true )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(147,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( ~ ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 ) )
= $false )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[143]) ).
thf(148,plain,
! [SV18: $i,SV14: $i,SV6: $i,SV25: $i,SV24: $i,SV21: $i] :
( ( ( SV21
= ( ordered_pair @ SV24 @ SV25 ) )
= $false )
| ( ( in @ SV24 @ SV6 )
= $false )
| ( ( in @ SV25 @ SV14 )
= $false )
| ( ( in @ SV21 @ SV18 )
= $true )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(149,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( in @ ( sK7_E @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV6 )
= $true )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(150,plain,
! [SV6: $i,SV14: $i,SV18: $i,SV22: $i] :
( ( ( in @ ( sK8_SY27 @ SV22 @ SV18 @ SV14 @ SV6 ) @ SV14 )
= $true )
| ( ( in @ SV22 @ SV18 )
= $false )
| ( ( SV18
= ( cartesian_product2 @ SV6 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(151,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[43,150,149,148,144,140,137,136,122,106,105,98,77,67,61,60,56,55,54,46]) ).
thf(152,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(153,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(154,plain,
( ( ! [A: $i] :
( ! [B: $i,C: $i] :
( ( ( ! [SY28: $i,SY29: $i] :
( ~ ( in @ SY28 @ A )
| ~ ( in @ SY29 @ B )
| ( ( sK9_D @ C @ B @ A )
!= ( ordered_pair @ SY28 @ SY29 ) ) )
| ~ ( in @ ( sK9_D @ C @ B @ A ) @ C ) )
& ( ( ( in @ ( sK10_SY30 @ C @ B @ A ) @ A )
& ( in @ ( sK11_SY32 @ C @ B @ A ) @ B )
& ( ( sK9_D @ C @ B @ A )
= ( ordered_pair @ ( sK10_SY30 @ C @ B @ A ) @ ( sK11_SY32 @ C @ B @ A ) ) ) )
| ( in @ ( sK9_D @ C @ B @ A ) @ C ) ) )
| ( C
= ( cartesian_product2 @ A @ B ) ) )
& ! [B: $i,C: $i] :
( ( C
!= ( cartesian_product2 @ A @ B ) )
| ( ! [D: $i] :
( ! [E: $i,F: $i] :
( ~ ( in @ E @ A )
| ~ ( in @ F @ B )
| ( D
!= ( ordered_pair @ E @ F ) ) )
| ( in @ D @ C ) )
& ! [D: $i] :
( ~ ( in @ D @ C )
| ( ( in @ ( sK7_E @ D @ C @ B @ A ) @ A )
& ( in @ ( sK8_SY27 @ D @ C @ B @ A ) @ B )
& ( D
= ( ordered_pair @ ( sK7_E @ D @ C @ B @ A ) @ ( sK8_SY27 @ D @ C @ B @ A ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(155,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK6_C @ B @ A ) @ A )
& ~ ( in @ ( sK6_C @ B @ A ) @ B ) )
| ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(156,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(157,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(158,plain,
( ( empty @ sK5_A )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(159,plain,
( ( ~ ( empty @ sK4_A ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(160,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(161,plain,
( ( subset @ sK1_A @ sK2_SY24 )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(162,plain,
( ( ~ ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(163,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( ~ ( ! [SX3: $i,SX4: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX4 @ SX1 )
| ( ( sK9_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ SX3 @ SX4 ) ) )
| ~ ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK11_SY32 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( ( sK9_D @ SX2 @ SX1 @ SX0 )
!= ( ordered_pair @ ( sK10_SY30 @ SX2 @ SX1 @ SX0 ) @ ( sK11_SY32 @ SX2 @ SX1 @ SX0 ) ) ) )
| ( in @ ( sK9_D @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX2
= ( cartesian_product2 @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ( SX2
!= ( cartesian_product2 @ SX0 @ SX1 ) )
| ~ ( ~ ! [SX3: $i] :
( ! [SX4: $i,SX5: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX5 @ SX1 )
| ( SX3
!= ( ordered_pair @ SX4 @ SX5 ) ) )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK8_SY27 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ( SX3
!= ( ordered_pair @ ( sK7_E @ SX3 @ SX2 @ SX1 @ SX0 ) @ ( sK8_SY27 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(164,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(165,plain,
! [SV26: $i] :
( ( ! [SY69: $i] :
( ~ ( in @ SV26 @ SY69 )
| ~ ( in @ SY69 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(166,plain,
! [SV27: $i] :
( ( ! [SY70: $i] :
( ( unordered_pair @ SV27 @ SY70 )
= ( unordered_pair @ SY70 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(167,plain,
! [SV28: $i] :
( ( ! [SY71: $i] :
( ( ordered_pair @ SV28 @ SY71 )
= ( unordered_pair @ ( unordered_pair @ SV28 @ SY71 ) @ ( singleton @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(168,plain,
! [SV29: $i] :
( ( ! [SY72: $i] :
~ ( empty @ ( ordered_pair @ SV29 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(169,plain,
( ( empty @ sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV30: $i] :
( ( subset @ SV30 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(171,plain,
( ( subset @ ( cartesian_product2 @ sK3_SY26 @ sK1_A ) @ ( cartesian_product2 @ sK3_SY26 @ sK2_SY24 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(172,plain,
! [SV31: $i] :
( ( ~ ( ~ ! [SY73: $i,SY74: $i] :
( ~ ( ~ ( ! [SY75: $i,SY76: $i] :
( ~ ( in @ SY75 @ SV31 )
| ~ ( in @ SY76 @ SY73 )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
| ~ ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) @ SY73 ) )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) ) )
| ( SY74
= ( cartesian_product2 @ SV31 @ SY73 ) ) )
| ~ ! [SY77: $i,SY78: $i] :
( ( SY78
!= ( cartesian_product2 @ SV31 @ SY77 ) )
| ~ ( ~ ! [SY79: $i] :
( ! [SY80: $i,SY81: $i] :
( ~ ( in @ SY80 @ SV31 )
| ~ ( in @ SY81 @ SY77 )
| ( SY79
!= ( ordered_pair @ SY80 @ SY81 ) ) )
| ( in @ SY79 @ SY78 ) )
| ~ ! [SY82: $i] :
( ~ ( in @ SY82 @ SY78 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) @ SY77 ) )
| ( SY82
!= ( ordered_pair @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(173,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(174,plain,
! [SV32: $i,SV26: $i] :
( ( ~ ( in @ SV26 @ SV32 )
| ~ ( in @ SV32 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV33: $i,SV27: $i] :
( ( ( unordered_pair @ SV27 @ SV33 )
= ( unordered_pair @ SV33 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV34: $i,SV28: $i] :
( ( ( ordered_pair @ SV28 @ SV34 )
= ( unordered_pair @ ( unordered_pair @ SV28 @ SV34 ) @ ( singleton @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV35: $i,SV29: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV29 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(178,plain,
! [SV31: $i] :
( ( ~ ! [SY73: $i,SY74: $i] :
( ~ ( ~ ( ! [SY75: $i,SY76: $i] :
( ~ ( in @ SY75 @ SV31 )
| ~ ( in @ SY76 @ SY73 )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
| ~ ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) @ SY73 ) )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) ) )
| ( SY74
= ( cartesian_product2 @ SV31 @ SY73 ) ) )
| ~ ! [SY77: $i,SY78: $i] :
( ( SY78
!= ( cartesian_product2 @ SV31 @ SY77 ) )
| ~ ( ~ ! [SY79: $i] :
( ! [SY80: $i,SY81: $i] :
( ~ ( in @ SY80 @ SV31 )
| ~ ( in @ SY81 @ SY77 )
| ( SY79
!= ( ordered_pair @ SY80 @ SY81 ) ) )
| ( in @ SY79 @ SY78 ) )
| ~ ! [SY82: $i] :
( ~ ( in @ SY82 @ SY78 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) @ SY77 ) )
| ( SY82
!= ( ordered_pair @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(179,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(180,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[173]) ).
thf(181,plain,
! [SV32: $i,SV26: $i] :
( ( ( ~ ( in @ SV26 @ SV32 ) )
= $true )
| ( ( ~ ( in @ SV32 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(182,plain,
! [SV35: $i,SV29: $i] :
( ( empty @ ( ordered_pair @ SV29 @ SV35 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(183,plain,
! [SV31: $i] :
( ( ~ ! [SY73: $i,SY74: $i] :
( ~ ( ~ ( ! [SY75: $i,SY76: $i] :
( ~ ( in @ SY75 @ SV31 )
| ~ ( in @ SY76 @ SY73 )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
| ~ ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) @ SY73 ) )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) ) )
| ( SY74
= ( cartesian_product2 @ SV31 @ SY73 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(184,plain,
! [SV31: $i] :
( ( ~ ! [SY77: $i,SY78: $i] :
( ( SY78
!= ( cartesian_product2 @ SV31 @ SY77 ) )
| ~ ( ~ ! [SY79: $i] :
( ! [SY80: $i,SY81: $i] :
( ~ ( in @ SY80 @ SV31 )
| ~ ( in @ SY81 @ SY77 )
| ( SY79
!= ( ordered_pair @ SY80 @ SY81 ) ) )
| ( in @ SY79 @ SY78 ) )
| ~ ! [SY82: $i] :
( ~ ( in @ SY82 @ SY78 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) @ SY77 ) )
| ( SY82
!= ( ordered_pair @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(185,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK6_C @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(186,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(187,plain,
! [SV32: $i,SV26: $i] :
( ( ( in @ SV26 @ SV32 )
= $false )
| ( ( ~ ( in @ SV32 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(188,plain,
! [SV31: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ~ ( ~ ( ! [SY75: $i,SY76: $i] :
( ~ ( in @ SY75 @ SV31 )
| ~ ( in @ SY76 @ SY73 )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ SY75 @ SY76 ) ) )
| ~ ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) @ SY73 ) )
| ( ( sK9_D @ SY74 @ SY73 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SY74 @ SY73 @ SV31 ) @ ( sK11_SY32 @ SY74 @ SY73 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SY74 @ SY73 @ SV31 ) @ SY74 ) ) )
| ( SY74
= ( cartesian_product2 @ SV31 @ SY73 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(189,plain,
! [SV31: $i] :
( ( ! [SY77: $i,SY78: $i] :
( ( SY78
!= ( cartesian_product2 @ SV31 @ SY77 ) )
| ~ ( ~ ! [SY79: $i] :
( ! [SY80: $i,SY81: $i] :
( ~ ( in @ SY80 @ SV31 )
| ~ ( in @ SY81 @ SY77 )
| ( SY79
!= ( ordered_pair @ SY80 @ SY81 ) ) )
| ( in @ SY79 @ SY78 ) )
| ~ ! [SY82: $i] :
( ~ ( in @ SY82 @ SY78 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) @ SY77 ) )
| ( SY82
!= ( ordered_pair @ ( sK7_E @ SY82 @ SY78 @ SY77 @ SV31 ) @ ( sK8_SY27 @ SY82 @ SY78 @ SY77 @ SV31 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(190,plain,
! [SV36: $i] :
( ( ! [SY83: $i] :
( ~ ( ~ ( in @ ( sK6_C @ SY83 @ SV36 ) @ SV36 )
| ~ ~ ( in @ ( sK6_C @ SY83 @ SV36 ) @ SY83 ) )
| ( subset @ SV36 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(191,plain,
! [SV37: $i] :
( ( ! [SY84: $i] :
( ~ ( subset @ SV37 @ SY84 )
| ! [SY85: $i] :
( ~ ( in @ SY85 @ SV37 )
| ( in @ SY85 @ SY84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(192,plain,
! [SV26: $i,SV32: $i] :
( ( ( in @ SV32 @ SV26 )
= $false )
| ( ( in @ SV26 @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(193,plain,
! [SV38: $i,SV31: $i] :
( ( ! [SY86: $i] :
( ~ ( ~ ( ! [SY87: $i,SY88: $i] :
( ~ ( in @ SY87 @ SV31 )
| ~ ( in @ SY88 @ SV38 )
| ( ( sK9_D @ SY86 @ SV38 @ SV31 )
!= ( ordered_pair @ SY87 @ SY88 ) ) )
| ~ ( in @ ( sK9_D @ SY86 @ SV38 @ SV31 ) @ SY86 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SY86 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SY86 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SY86 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SY86 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SY86 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SY86 @ SV38 @ SV31 ) @ SY86 ) ) )
| ( SY86
= ( cartesian_product2 @ SV31 @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(194,plain,
! [SV39: $i,SV31: $i] :
( ( ! [SY89: $i] :
( ( SY89
!= ( cartesian_product2 @ SV31 @ SV39 ) )
| ~ ( ~ ! [SY90: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY90
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY90 @ SY89 ) )
| ~ ! [SY93: $i] :
( ~ ( in @ SY93 @ SY89 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY93 @ SY89 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY93 @ SY89 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY93
!= ( ordered_pair @ ( sK7_E @ SY93 @ SY89 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY93 @ SY89 @ SV39 @ SV31 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(195,plain,
! [SV36: $i,SV40: $i] :
( ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV36 )
| ~ ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 ) )
| ( subset @ SV36 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(196,plain,
! [SV41: $i,SV37: $i] :
( ( ~ ( subset @ SV37 @ SV41 )
| ! [SY94: $i] :
( ~ ( in @ SY94 @ SV37 )
| ( in @ SY94 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(197,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ~ ( ~ ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) )
| ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) ) )
| ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(198,plain,
! [SV39: $i,SV31: $i,SV43: $i] :
( ( ( SV43
!= ( cartesian_product2 @ SV31 @ SV39 ) )
| ~ ( ~ ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(199,plain,
! [SV36: $i,SV40: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV36 )
| ~ ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 ) ) )
= $true )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(200,plain,
! [SV41: $i,SV37: $i] :
( ( ( ~ ( subset @ SV37 @ SV41 ) )
= $true )
| ( ( ! [SY94: $i] :
( ~ ( in @ SY94 @ SV37 )
| ( in @ SY94 @ SV41 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(201,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( ~ ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) )
| ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) ) ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(202,plain,
! [SV39: $i,SV31: $i,SV43: $i] :
( ( ( ( SV43
!= ( cartesian_product2 @ SV31 @ SV39 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(203,plain,
! [SV36: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV36 )
| ~ ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 ) )
= $false )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(204,plain,
! [SV41: $i,SV37: $i] :
( ( ( subset @ SV37 @ SV41 )
= $false )
| ( ( ! [SY94: $i] :
( ~ ( in @ SY94 @ SV37 )
| ( in @ SY94 @ SV41 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(205,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) )
| ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
| ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) ) )
= $false )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(206,plain,
! [SV39: $i,SV31: $i,SV43: $i] :
( ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false )
| ( ( ~ ( ~ ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(207,plain,
! [SV36: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV36 ) )
= $false )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(208,plain,
! [SV36: $i,SV40: $i] :
( ( ( ~ ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 ) )
= $false )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[203]) ).
thf(209,plain,
! [SV41: $i,SV37: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV37 )
| ( in @ SV44 @ SV41 ) )
= $true )
| ( ( subset @ SV37 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ( ~ ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) )
| ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) ) )
= $false )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) ) )
= $false )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[205]) ).
thf(212,plain,
! [SV43: $i,SV39: $i,SV31: $i] :
( ( ( ~ ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) )
| ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(213,plain,
! [SV36: $i,SV40: $i] :
( ( ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV36 )
= $true )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(214,plain,
! [SV36: $i,SV40: $i] :
( ( ( ~ ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 ) )
= $true )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(215,plain,
! [SV41: $i,SV37: $i,SV44: $i] :
( ( ( ~ ( in @ SV44 @ SV37 ) )
= $true )
| ( ( in @ SV44 @ SV41 )
= $true )
| ( ( subset @ SV37 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(216,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) )
| ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(217,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
| ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(218,plain,
! [SV43: $i,SV39: $i,SV31: $i] :
( ( ( ~ ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) ) )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(219,plain,
! [SV31: $i,SV39: $i,SV43: $i] :
( ( ( ~ ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(220,plain,
! [SV36: $i,SV40: $i] :
( ( ( in @ ( sK6_C @ SV40 @ SV36 ) @ SV40 )
= $false )
| ( ( subset @ SV36 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(221,plain,
! [SV41: $i,SV37: $i,SV44: $i] :
( ( ( in @ SV44 @ SV37 )
= $false )
| ( ( in @ SV44 @ SV41 )
= $true )
| ( ( subset @ SV37 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(222,plain,
! [SV42: $i,SV38: $i,SV31: $i] :
( ( ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY95 @ SV31 )
| ~ ( in @ SY96 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SY95 @ SY96 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(223,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(224,plain,
! [SV43: $i,SV39: $i,SV31: $i] :
( ( ( ! [SY97: $i] :
( ! [SY91: $i,SY92: $i] :
( ~ ( in @ SY91 @ SV31 )
| ~ ( in @ SY92 @ SV39 )
| ( SY97
!= ( ordered_pair @ SY91 @ SY92 ) ) )
| ( in @ SY97 @ SV43 ) ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(225,plain,
! [SV31: $i,SV39: $i,SV43: $i] :
( ( ( ! [SY100: $i] :
( ~ ( in @ SY100 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SY100
!= ( ordered_pair @ ( sK7_E @ SY100 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SY100 @ SV43 @ SV39 @ SV31 ) ) ) ) ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(226,plain,
! [SV42: $i,SV38: $i,SV31: $i,SV45: $i] :
( ( ( ! [SY101: $i] :
( ~ ( in @ SV45 @ SV31 )
| ~ ( in @ SY101 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SY101 ) ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(227,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(228,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV31: $i] :
( ( ( ! [SY102: $i,SY103: $i] :
( ~ ( in @ SY102 @ SV31 )
| ~ ( in @ SY103 @ SV39 )
| ( SV46
!= ( ordered_pair @ SY102 @ SY103 ) ) )
| ( in @ SV46 @ SV43 ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(229,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV43 )
| ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SV47
!= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) ) ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(230,plain,
! [SV42: $i,SV38: $i,SV48: $i,SV31: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV31 )
| ~ ( in @ SV48 @ SV38 )
| ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(231,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(232,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(233,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV31: $i] :
( ( ( ! [SY102: $i,SY103: $i] :
( ~ ( in @ SY102 @ SV31 )
| ~ ( in @ SY103 @ SV39 )
| ( SV46
!= ( ordered_pair @ SY102 @ SY103 ) ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(234,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( in @ SV47 @ SV43 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SV47
!= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) ) ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(235,plain,
! [SV42: $i,SV38: $i,SV48: $i,SV31: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV31 )
| ~ ( in @ SV48 @ SV38 ) )
= $true )
| ( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(236,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(237,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
= ( ordered_pair @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) ) )
= $true )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[232]) ).
thf(238,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV31: $i,SV49: $i] :
( ( ( ! [SY104: $i] :
( ~ ( in @ SV49 @ SV31 )
| ~ ( in @ SY104 @ SV39 )
| ( SV46
!= ( ordered_pair @ SV49 @ SY104 ) ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(239,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( in @ SV47 @ SV43 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SV47
!= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) ) ) )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(240,plain,
! [SV42: $i,SV38: $i,SV48: $i,SV31: $i,SV45: $i] :
( ( ( ~ ( in @ SV45 @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV48 @ SV38 ) )
= $true )
| ( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(241,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(242,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV50: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV31 )
| ~ ( in @ SV50 @ SV39 )
| ( SV46
!= ( ordered_pair @ SV49 @ SV50 ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(243,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
| ( SV47
!= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(244,plain,
! [SV42: $i,SV38: $i,SV48: $i,SV31: $i,SV45: $i] :
( ( ( in @ SV45 @ SV31 )
= $false )
| ( ( ~ ( in @ SV48 @ SV38 ) )
= $true )
| ( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(245,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(246,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( ~ ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 ) )
= $false )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(247,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV50: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV31 )
| ~ ( in @ SV50 @ SV39 ) )
= $true )
| ( ( ( SV46
!= ( ordered_pair @ SV49 @ SV50 ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(248,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(249,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ( SV47
!= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(250,plain,
! [SV42: $i,SV31: $i,SV45: $i,SV38: $i,SV48: $i] :
( ( ( in @ SV48 @ SV38 )
= $false )
| ( ( in @ SV45 @ SV31 )
= $false )
| ( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
!= ( ordered_pair @ SV45 @ SV48 ) ) )
= $true )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(251,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( in @ ( sK10_SY30 @ SV42 @ SV38 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(252,plain,
! [SV31: $i,SV38: $i,SV42: $i] :
( ( ( in @ ( sK11_SY32 @ SV42 @ SV38 @ SV31 ) @ SV38 )
= $true )
| ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(253,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV50: $i,SV31: $i,SV49: $i] :
( ( ( ~ ( in @ SV49 @ SV31 ) )
= $true )
| ( ( ~ ( in @ SV50 @ SV39 ) )
= $true )
| ( ( ( SV46
!= ( ordered_pair @ SV49 @ SV50 ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(254,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) ) )
= $true )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(255,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( SV47
= ( ordered_pair @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) ) )
= $true )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(256,plain,
! [SV48: $i,SV45: $i,SV31: $i,SV38: $i,SV42: $i] :
( ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
= ( ordered_pair @ SV45 @ SV48 ) )
= $false )
| ( ( in @ SV45 @ SV31 )
= $false )
| ( ( in @ SV48 @ SV38 )
= $false )
| ( ( ~ ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 ) )
= $true )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[250]) ).
thf(257,plain,
! [SV43: $i,SV46: $i,SV39: $i,SV50: $i,SV31: $i,SV49: $i] :
( ( ( in @ SV49 @ SV31 )
= $false )
| ( ( ~ ( in @ SV50 @ SV39 ) )
= $true )
| ( ( ( SV46
!= ( ordered_pair @ SV49 @ SV50 ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(258,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
| ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(259,plain,
! [SV45: $i,SV48: $i,SV31: $i,SV38: $i,SV42: $i] :
( ( ( in @ ( sK9_D @ SV42 @ SV38 @ SV31 ) @ SV42 )
= $false )
| ( ( in @ SV48 @ SV38 )
= $false )
| ( ( in @ SV45 @ SV31 )
= $false )
| ( ( ( sK9_D @ SV42 @ SV38 @ SV31 )
= ( ordered_pair @ SV45 @ SV48 ) )
= $false )
| ( ( SV42
= ( cartesian_product2 @ SV31 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(260,plain,
! [SV43: $i,SV46: $i,SV31: $i,SV49: $i,SV39: $i,SV50: $i] :
( ( ( in @ SV50 @ SV39 )
= $false )
| ( ( in @ SV49 @ SV31 )
= $false )
| ( ( ( SV46
!= ( ordered_pair @ SV49 @ SV50 ) ) )
= $true )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(261,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(262,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 ) )
= $false )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(263,plain,
! [SV43: $i,SV39: $i,SV31: $i,SV50: $i,SV49: $i,SV46: $i] :
( ( ( SV46
= ( ordered_pair @ SV49 @ SV50 ) )
= $false )
| ( ( in @ SV49 @ SV31 )
= $false )
| ( ( in @ SV50 @ SV39 )
= $false )
| ( ( in @ SV46 @ SV43 )
= $true )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(264,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( in @ ( sK7_E @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV31 )
= $true )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(265,plain,
! [SV31: $i,SV39: $i,SV43: $i,SV47: $i] :
( ( ( in @ ( sK8_SY27 @ SV47 @ SV43 @ SV39 @ SV31 ) @ SV39 )
= $true )
| ( ( in @ SV47 @ SV43 )
= $false )
| ( ( SV43
= ( cartesian_product2 @ SV31 @ SV39 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(266,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[158,265,264,263,259,255,252,251,237,221,220,213,192,182,176,175,171,170,169,161]) ).
thf(267,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[266,151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 23:03:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 9
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:9,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:11,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.57/0.98
% 0.57/0.98 ********************************
% 0.57/0.98 * All subproblems solved! *
% 0.57/0.98 ********************************
% 0.57/0.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:266,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/1.02
% 0.57/1.02 %**** Beginning of derivation protocol ****
% 0.57/1.02 % SZS output start CNFRefutation
% See solution above
% 0.85/1.02
% 0.85/1.02 %**** End of derivation protocol ****
% 0.85/1.02 %**** no. of clauses in derivation: 267 ****
% 0.85/1.02 %**** clause counter: 266 ****
% 0.85/1.02
% 0.85/1.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:266,loop_count:0,foatp_calls:1,translation:fof_full)
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